The word God is a proof that God exist? (sic)
Not sure if that question on Facebook was supposed to be a question or a statement. I think that it was supposed to be a leading question, as in leading the reader to go along with the false presumption that a god exists because the word “God” exists.
Lots of words exist. That doesn’t mean that the thing represented by the word exists. I’m sure that you and I can come up with many examples, like Unicorn, Horcrux, Fairy, Leprechaun, Mermaid, cyclops, ogre, etc.